Final answer:
To find the original cost of a digital home theater system and a 40-inch high definition television before a 6.75% sales tax that made the total $2668.75, divide the total by 1.0675 to get $2500.
Step-by-step explanation:
The question is asking us to find the original cost of the television and home theater system before tax was added. To calculate this, we need to remove the sales tax from the total cost. Let's denote the original price as 'P'. The total cost, including sales tax, is $2668.75. Sales tax is 6.75% of the original cost, which means the equation we will solve is P + 0.0675P = $2668.75. Simplifying this, we get 1.0675P = $2668.75. Dividing both sides by 1.0675 will give us the original price, P, of the television and home theater system.
To find the original cost, we perform the calculation:
P = $2668.75 / 1.0675 = $2500 (rounded to the nearest dollar)
So, the original cost of the television and theater system, before tax, was $2500.